Question

3. How many factors does a product of three distinct primes
have? What about a product of 4 distinct primes?​

Answer 1

Answer:

The answer is 8. There is a quick way to work out the number of factors of any number.

Since every integer greater than 1 can be written uniquely as the product of primes, we can write a number (n) as

n=(p1)^(a1) * (p2)^(a2) * … * (pn)^(an) where px and ax ather the xth prime and exponent respectively

So the number of different factors are (a1+1)(a2+1)…(an+1)

Example number of factors of 360 (2^4 * 3^3 * 5^1) is (4+1 )*(2+1)*(1+1)=5*3*2=30

In your question, the number was the product of 3 different primes, so it’s n=(p1)^1 * (p2)^1 * (p3)^1 so the number of factors is (1+1)*(1+1)*(1+1)=2*2*2=8